Data-driven identification of a model from data can take many different forms. The SINDy [1]} algorithm requires an a priori choice of basis, e.g. the monomials or the rational functions. This dictionary is then used to construct an ODE (or PDE) using a least squares regression. While this gives a generative model learned from the data, which can give point predictions of future values, there does not seem to be a method giving confidence bounds on these point predictions. Alternatively, the Bayesian system identification [2]} formulates the problem as a hidden Markov model and claims to subsume the classical dynamic mode decomposition (DMD) and sparse DMD in its formulation [2]}.
